Open Middle®
Directions: Using the integers -9 to 9, at most one time each, place an integer in each box to make a real number product with the greatest possible value.
Hint
What is the difference between a real and complex number? What causes an i to go away during multiplication? What causes a term to go away during binomial multiplication? How do we choose integers such that the i terms are additive inverses of one another?
Answer
There are two possible answers: (-9 + 6i)(-6 + -4i) and (9 + -6i)(6 + 4i)
Source: Robert Kaplinsky in Open Middle Math
How can we prove that this is the biggest product possible?